Is there a floor drain or any other drain nearby that is not used often? Sometimes the p-trap in a drain will dry out and allow sewer gas to escape. The smell becomes more intense when hot water goes down the drain.
This sounds like a typical well system problem, where tank pressure has decreased and the pump is constantly coming on.
water pressure
Low water pressure or cold water main undersized.
You have to undo the aerator at the end of the faucet and clean the screen or plastic water saver out. It will be plugged with sand or sediment.
A leak in the supply pipe.
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The simplest and lowest cost solution is to replace the shower head with one designed to increase the pressure.
check for leaks
If you mean a well tank, the water is forced in by the pump. The residual air pressure pushes the water out to the faucets.
No.
If your water pressure is low at all faucets, you can buy a gauge to fit faucets threaded for garden hose, they are about $10. You pressure should be 40-55psi. If pressure is low at all faucets, you may have a faulty PRV. This is the bell shaped regulator usually fitted where the water enters the building. A plumber can change these easily. Part costs about $60 and takes an hour to change -I do many and they are usually simple to change. If the pressure is low at just one faucet then remove and change the aerator. If that doesn't fix the problem you have a blockage in the shut off valve below it.
Air in the water lines to the upstairs. Not enough water pressure.